How to interpret goodness of Fit of GLM with gamma?

Question

I'm using SPSS to create a model of y (dependent variable: 0,11;0,234;0,2324) and five independent variables. I get the following results:

Deviance = 0,20 (value/df); 
Pearson chi-square = (0,50); Log Likelihood = -200,454;

Omnibus test:
Likelihood ratio chi-square - sig = 0.000. 

According with SPSS, this last test indicates that this model overcomes the null model. What does it means?

Should I calculate pseudo R^2?

I'm new in this kind of models, so it's hard for me to interpret them. I found some articles, but they all about Poisson distribution.

PS: if you know about any useful books, I appreciate!

Thanks!

Answer 1

I believe in SPSS the omnibus test compares the fitted model to an intercept-only model. The pseudo r-squared will tell you the percentage of variation in the data explained by the model (explained deviance, see Dobson 2002). In addition to Dobson (2002), you might want to refer to McCullagh and Nelder (1989). If your data are ecological in nature, I highly recommend Zuur et al. (2009). You will also want to plot your data--observed versus predicted, residuals, etc. as additional ways to evaluate the fit.

References

McCullagh, P., and J.A. Nelder. 1989. Generalized linear models. Chapman and Hall, New York. 511 p. Available (February 2020): http://www.utstat.toronto.edu/~brunner/oldclass/2201s11/readings/glmbook.pdf

Dobson, A.J. 2002. An introduction to generalized linear models, second edition. Chapman & Hall/CRC, Boca Raton. 221 p. Available (February 2020): https://reneues.files.wordpress.com/2010/01/an-introduction-to-generalized-linear-models-second-edition-dobson.pdf

Zuur, A.F., E.N. Ieno, N.J. Walker, A.A. Saveliev, and G.M. Smith. 2009. Mixed effects models and extensions in ecology with R. Springer. 574 p.